Hi Janet,
All of the standard rooms in the Walt Disney World value resorts, including Art of Animation, come equipped with two double beds or a one king. I'm a fan of the value resorts and stay there often, but having a smaller bed can be a bit uncomfortable in some situations.
For two queen beds, you will want to look at a moderate or deluxe resort. In your situation,
Port Orleans Riverside may be just the ticket. Most of those rooms come not only with two queen beds, but also have a fold out day bed that accommodates a child. The resort also has a number of amenities that will appeal to a youngster, including great pools and a playground.
A family suite at
Art of Animation might also work for you. The suites have a separate bedroom with a queen bed and two fold-out double beds in the living area. The biggest selling point for me -- besides the amazing themed decor -- is that each suite comes with two full bathrooms, a nice advantage when you are sharing a room among four people. The suites also have kitchenettes, including a small refrigerator and a microwave.
I have one other thought. Now that they are older, our daughters no longer like to share a bed, particularly a double, so we get a rollaway for one of them when we all four are staying at a value resort. It's a tight squeeze, but it does solve the bed problem. That could be an option if you find a value resort better fits your budget.
I hope that's helpful and gives you the information you need to find a room that will be comfortable for you and the rest of your family. Please let me know if I can answer any other questions for you as you plan your visit. Enjoy!
Wilma